If the system of linear equation $$3 x-2 y+z=2, 4 x-3 y+3 z=-5$$ and $$7 x-5 y+\lambda z=9$$ has no solution, then $$\lambda$$ equals to

Let $$A=\left[\begin{array}{lll}3 & 2 & 3 \\ 4 & 1 & 0 \\ 2 & 5 & 1\end{array}\right]$$ and $$49 B=\left[\begin{array}{ccc}1 & 13 & -3 \\ -4 & -3 & 12 \\ \alpha & -11 & -5\end{array}\right]$$ If $$B$$ is the inverse of $$A$$, then the value of $$\alpha$$ is

$$ \text { If } A=\left[\begin{array}{cc} \sin \theta & -\cos \theta \\ \cos \theta & \sin \theta \end{array}\right] \text {, then } A(\operatorname{adj} A)^{-1} \text { equals to } $$

If $$a, b, c$$ are non-zero real numbers and if the system of equations $$(a-1) x-y-z=0, -x+(b-1) y-z=0,-x-y+(c-1) z=0$$ has a non-trivial solution, then $$a b+b c+c a$$ equals to